The lentiviruses HIV and simian immunodeficiency virus (SIV) subvert intracellular membrane traffic as part of their replication cycle. The lentiviral Nef protein helps viruses evade innate and adaptive immune defenses by hijacking the adaptor protein 1 (AP-1) and AP-2 clathrin adaptors. We found that HIV-1 Nef and the guanosine triphosphatase Arf1 induced trimerization and activation of AP-1. Here we report the cryo-electron microscopy structures of the Nef- and Arf1-bound AP-1 trimer in the active and inactive states. A central nucleus of three Arf1 molecules organizes the trimers. We combined the open trimer with a known dimer structure and thus predicted a hexagonal assembly with inner and outer faces that bind the membranes and clathrin, respectively. Hexagons were directly visualized and the model validated by reconstituting clathrin cage assembly. Arf1 and Nef thus play interconnected roles in allosteric activation, cargo recruitment, and coat assembly, revealing an unexpectedly intricate organization of the inner AP-1 layer of the clathrin coat.